Now, more than a decade after Ms. Rudolph left the show, and five years since Mr. Armisen’s departure, they are back together, in the new Amazon comedy “Forever.” But this time, they’re playing a relatively normal married couple who argue about fork tines.

Their new show, which debuts Sept. 14 and is written and produced by the Emmy-winning writers Alan Yang (“Master of None”) and Matt Hubbard (“30 Rock”), signals a big leap from the pair’s sketch-comedy roots. Instead of playing a multitude of outlandish characters on a series with no discernible end (“S.N.L.” is entering its 44th season), the two play a single character each in a comedy capped at eight episodes.

“Alan said it was the first time he did a show that had an ending, where he knew where it was going,” Ms. Rudolph said. “That was a huge light bulb for Fred and myself. We both said, ‘Yes, that’s what we want.’ ”

The show began coming together in March 2017, when Mr. Armisen and Ms. Rudolph approached Mr. Yang about creating a series for them. Mr. Armisen was wrapping up his sketch series “Portlandia” after eight seasons; Ms. Rudolph was coming off her short-lived variety series with Martin Short, “Maya & Marty.” And they had always shared a desire to do another show together. “I remember Fred reminding me, weren’t we going to do a show where we played monsters or something?” Ms. Rudolph said.

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Ms. Rudolph and Mr. Armisen combined on numerous skits on “Saturday Night Live,” including playing Beyoncé and Prince.CreditDana Edelson/NBC

Mr. Yang immediately contacted Mr. Hubbard, whom he had worked with on “Parks and Recreation.” The two began brainstorming ideas and presented the actors with several pitches, between “five or so” (Mr. Armisen’s estimate) and “a million” (Ms. Rudolph’s count). Maybe Maya and Fred could be friends, they thought, or they could be dating, or they could be brother and sister?

“There was one that had them running a preschool for rich people in Silver Lake,” Mr. Hubbard recalled, sitting in a trailer here with Mr. Yang during a break in filming the series. “I think I pitched a show where they were leaders of a cult.”

“That was actually one of the better ideas,” Mr. Yang said.

In the winning scenario, Mr. Armisen is Oscar, a dentist in Riverside, Calif., Mr. Yang’s hometown. June, Ms. Rudolph’s character, works at a shady time-share company when she isn’t chickening out of trying to find something better. “I think we thought it would be fun to take two people who are unbelievably good at playing anybody, and have them play a relatively normcore couple in Riverside,” Mr. Hubbard said.

But despite their satisfying if somewhat predictable existence in a sleepy suburban Southern California town, June and Oscar find themselves dealing with improbable tragedies, energy-giving fountains and a mysterious briefcase-wielding weirdo.

The two were drawn to the series’ unusual story arc, which includes a series of life-changing moments early into the eight-episode run, and the chance to play a pair of characters who grow and change over time. “It’s really about the relationship,” Ms. Rudolph said. “They’re happy, and from the outside, I think everyone sees a loving relationship. But with June, she’s always wondering, what else is out there?”

Catherine Keener, who plays Kase, a free spirit who comes between the two, worked with Ms. Rudolph in the 2017 film “We Don’t Belong Here,” but had never worked with Mr. Armisen before. “Individually they’re both brilliant, but they’re another thing when they’re together,” she said. “You can almost see it, this thing, like they’re in this little pocket together. Everyone would stand around and just watch them.”

The series has offered both Ms. Rudolph and Mr. Armisen a chance to bust out of the sketch-comedy bubble. “I never thought when I started out that being in comedy would mean being limited to comedy,” she said. “But very quickly, when you demonstrate you can be funny, people label you as a comedian, and they don’t like it when you go outside of that box.”

The plotline of the series also allowed everyone involved to get outside for a change. On a chilly afternoon last March, Ms. Rudolph was here at the Leo Carrillo State Beach filming the final episode of the series. Over the course of the day, the actress flew a kite with Julia Ormond, jumped in and out of the Pacific and ran back and forth along the beach in front of Mr. Armisen. “He was off camera, and he was laughing so hard, because I don’t think he’s ever seen me run before,” Ms. Rudolph said.

Besides the Malibu beach, the shoots have taken the cast and crew all over the Los Angeles area, including Big Bear and Simi Valley. Mr. Armisen, who moved to California three years ago, has been able to explore the state on Amazon’s dime; for the producers, it’s been a chance to get out from under the faux fluorescent lighting of their previous sitcoms. “ ‘30 Rock’ is in an office, ‘Parks and Rec’ is in an office,” Hubbard recalled.

While Ms. Rudolph was flying her kite on the beach, Mr. Armisen hung out by a nearby craft services truck. As he waited for his next scene, he talked about how “S.N.L.,” “Portlandia” and “Forever” feel like extensions of each other (“As corny as it sounds, it’s sort of like a tree, like we’re still all united with all of that”), and why “America’s Funniest Home Videos” will always make him laugh (“I could mention some cool show from England, but as far as actual, immediate laughter, that show still works”).

And he talked about the one important advantage “Forever” has over many of his past sketch comedy gigs. “I don’t have to keep putting on different wigs and mustaches and stuff,” he said. “I’m just one character all the way through. I don’t have to think like, ‘Wait, who am I today?’ So that’s been a nice feeling.”

A version of this article appears in print on , Section AR, Page 13 of the New York edition with the headline: Here’s the Challenge: Be Relatively Normal. Order Reprints | Today’s Paper | Subscribe